Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20262573⋊C5 |
| Fitting, socle, derived, Hall | C112×C13 ⋊ C4×C5 |
| Hall | C13×#10597243 ⋊ C4 |
| Hall | #20262573 ⋊ C5 |
| Hall | #10597243 ⋊ #261 |
| Sylow | C112 ⋊ C5×#261 |
| Sylow | C13 ⋊ #92150⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C13 | C4×C5 |
| prime radical | C13⋊#11925892 | C2 |
| cosocle | C11⋊D143 | C2×C5 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 286 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2)(3,15,9,4,18,6,17,19,10,21,8,13,16,12,22,5,7,14,20,11)(24,25,26,28)(27,30,31,32)(29,34,35,33);(1,3,9,7,18,10,20,22,17,16,8)(2,11,15,5,4,19,14,12,6,13,21)(23,24,27,32,34,25,29,35,28,33,30,31,26)Polycyclic presentation:
2,5,2,11^2,13|a^2=c,d^a=d^5e^7,e^a=de^6,f^a=f^5,d^b=d^3,e^b=e^3,d^c=d^10,e^c=e^10,f^c=f^12113 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 96);